Hi,
Thanks for the great plugin!
I encountered a problem, which is not really severe but confusing. In the chat window there is an option to log out (why actually?). After clicking it, I'm asked whether I want to log out from WordPress. If I confirm, a full WordPress screen appears inside the chat frame (probably mistaking it for the whole browser window).
I run version 1.3.2.1 of the BuddyPress Chat Component and the above described happened when I was logged in as admin.

The chat does have a logout link. I pass to it the logout link that wordpress knows. The alternative is to hack the chat code and remove the logout link. I went with other way with it only because I didn't have to hack the core chat code.